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@ -18,50 +18,50 @@ record Cayley {0 k1,k2,k3 : Type} f (p : k1 -> k2 -> k3) a b where
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runCayley : f (p a b)
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public export
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export
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Functor f => Profunctor p => Profunctor (Cayley f p) where
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dimap f g (MkCayley p) = MkCayley (dimap f g <$> p)
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lmap f (MkCayley p) = MkCayley (lmap f <$> p)
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rmap g (MkCayley p) = MkCayley (rmap g <$> p)
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public export
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export
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Functor f => ProfunctorFunctor (Cayley f) where
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promap f (MkCayley p) = MkCayley (map f p)
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public export
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export
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Monad m => ProfunctorMonad (Cayley m) where
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propure = MkCayley . pure
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projoin (MkCayley p) = MkCayley $ p >>= runCayley
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public export
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export
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Functor f => GenStrong ten p => GenStrong ten (Cayley f p) where
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strongl (MkCayley p) = MkCayley (strongl {ten} <$> p)
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strongr (MkCayley p) = MkCayley (strongr {ten} <$> p)
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public export
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export
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Functor f => GenCostrong ten p => GenCostrong ten (Cayley f p) where
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costrongl (MkCayley p) = MkCayley (costrongl {ten} <$> p)
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costrongr (MkCayley p) = MkCayley (costrongr {ten} <$> p)
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public export
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export
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Functor f => Closed p => Closed (Cayley f p) where
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closed (MkCayley p) = MkCayley (closed <$> p)
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public export
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export
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Functor f => Traversing p => Traversing (Cayley f p) where
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traverse' (MkCayley p) = MkCayley (traverse' <$> p)
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wander f (MkCayley p) = MkCayley (wander f <$> p)
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public export
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export
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Functor f => Mapping p => Mapping (Cayley f p) where
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map' (MkCayley p) = MkCayley (map' <$> p)
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roam f (MkCayley p) = MkCayley (roam f <$> p)
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public export
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export
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Functor g => Sieve p f => Sieve (Cayley g p) (g . f) using Functor.Compose where
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sieve (MkCayley p) x = ($ x) . sieve <$> p
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public export
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mapCayley : (forall x. f x -> g x) -> Cayley f p :-> Cayley g p
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export
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mapCayley : (forall x. f x -> g x) -> Cayley f p a b -> Cayley g p a b
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mapCayley f (MkCayley p) = MkCayley (f p)
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|
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@ -26,26 +26,26 @@ interface Profunctor p => Closed p where
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------------------------------------------------------------------------------
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-- Implementations
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-- Implementations for existing types
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------------------------------------------------------------------------------
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public export
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export
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Closed Morphism where
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closed (Mor f) = Mor (f .)
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||| A named implementation of `Closed` for function types.
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||| Use this to avoid having to use a type wrapper like `Morphism`.
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public export
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export
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[Function] Closed (\a,b => a -> b) using Profunctor.Function where
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closed = (.)
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public export
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export
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Functor f => Closed (Costar f) where
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closed (MkCostar p) = MkCostar $ \f,x => p (map ($ x) f)
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public export
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export
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curry' : Closed p => p (a, b) c -> p a (b -> c)
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curry' = lmap (,) . closed
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@ -71,40 +71,40 @@ record Closure p a b where
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runClosure : forall x. p (x -> a) (x -> b)
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public export
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export
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Profunctor p => Profunctor (Closure p) where
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dimap f g (MkClosure p) = MkClosure $ dimap (f .) (g .) p
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lmap f (MkClosure p) = MkClosure $ lmap (f .) p
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rmap f (MkClosure p) = MkClosure $ rmap (f .) p
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public export
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export
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ProfunctorFunctor Closure where
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promap f (MkClosure p) = MkClosure (f p)
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public export
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export
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ProfunctorComonad Closure where
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proextract (MkClosure p) = dimap const ($ ()) p
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produplicate (MkClosure p) = MkClosure $ MkClosure $ dimap uncurry curry p
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public export
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export
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Strong p => GenStrong Pair (Closure p) where
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strongl (MkClosure p) = MkClosure $ dimap hither yon $ first p
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strongr (MkClosure p) = MkClosure $ dimap hither yon $ second p
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public export
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export
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Profunctor p => Closed (Closure p) where
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closed p = runClosure $ produplicate p
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public export
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export
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Profunctor p => Functor (Closure p a) where
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map = rmap
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public export
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export
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close : Closed p => p :-> q -> p :-> Closure q
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close f p = MkClosure $ f $ closed p
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public export
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export
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unclose : Profunctor q => p :-> Closure q -> p :-> q
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unclose f p = dimap const ($ ()) $ runClosure $ f p
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@ -121,17 +121,17 @@ data Environment : (p : Type -> Type -> Type) -> Type -> Type -> Type where
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MkEnv : ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b
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public export
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export
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Profunctor (Environment p) where
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dimap f g (MkEnv l m r) = MkEnv (g . l) m (r . f)
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lmap f (MkEnv l m r) = MkEnv l m (r . f)
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rmap g (MkEnv l m r) = MkEnv (g . l) m r
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public export
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export
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ProfunctorFunctor Environment where
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promap f (MkEnv l m r) = MkEnv l (f m) r
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public export
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export
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ProfunctorMonad Environment where
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propure p = MkEnv ($ ()) p const
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projoin (MkEnv {x=x',y=y',z=z'} l' (MkEnv {x,y,z} l m r) r') = MkEnv (ll . curry) m rr
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@ -141,12 +141,12 @@ ProfunctorMonad Environment where
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rr : a -> (z', z) -> x
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rr a (b, c) = r (r' a b) c
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public export
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export
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ProfunctorAdjunction Environment Closure where
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prounit p = MkClosure (MkEnv id p id)
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procounit (MkEnv l (MkClosure x) r) = dimap r l x
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public export
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export
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Closed (Environment p) where
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closed {x=x'} (MkEnv {x,y,z} l m r) = MkEnv l' m r'
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where
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@ -155,15 +155,15 @@ Closed (Environment p) where
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r' : (x' -> a) -> (z, x') -> x
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r' f (z,x) = r (f x) z
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public export
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export
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Profunctor p => Functor (Environment p a) where
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map = rmap
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public export
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export
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environment : Closed q => p :-> q -> Environment p :-> q
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environment f (MkEnv l m r) = dimap r l $ closed (f m)
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public export
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export
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unenvironment : Environment p :-> q -> p :-> q
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unenvironment f p = f (MkEnv ($ ()) p const)
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|
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@ -80,25 +80,15 @@ unright = costrongr {ten=Either}
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------------------------------------------------------------------------------
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-- Implementations
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-- Implementations for existing types
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------------------------------------------------------------------------------
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public export
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export
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GenCostrong Pair Tagged where
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costrongl (Tag (x,_)) = Tag x
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costrongr (Tag (_,x)) = Tag x
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public export
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GenCostrong Either (Forget r) where
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costrongl (MkForget k) = MkForget (k . Left)
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costrongr (MkForget k) = MkForget (k . Right)
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public export
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GenCostrong Pair (Coforget r) where
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costrongl (MkCoforget k) = MkCoforget (fst . k)
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costrongr (MkCoforget k) = MkCoforget (snd . k)
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------------------------------------------------------------------------------
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-- Cotambara
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@ -111,27 +101,27 @@ public export
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data GenCotambara : (ten, p : Type -> Type -> Type) -> Type -> Type -> Type where
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MkCotambara : GenCostrong ten q => q :-> p -> q a b -> GenCotambara ten p a b
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public export
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export
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Profunctor (GenCotambara ten p) where
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lmap f (MkCotambara n p) = MkCotambara n (lmap f p)
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rmap f (MkCotambara n p) = MkCotambara n (rmap f p)
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dimap f g (MkCotambara n p) = MkCotambara n (dimap f g p)
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public export
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export
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ProfunctorFunctor (GenCotambara ten) where
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promap f (MkCotambara n p) = MkCotambara (f . n) p
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public export
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export
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GenCostrong ten (GenCotambara ten p) where
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costrongl (MkCotambara @{costr} n p) = MkCotambara n (costrongl @{costr} p)
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costrongr (MkCotambara @{costr} n p) = MkCotambara n (costrongr @{costr} p)
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public export
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export
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ProfunctorComonad (GenCotambara ten) where
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proextract (MkCotambara n p) = n p
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produplicate (MkCotambara n p) = MkCotambara id (MkCotambara n p)
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public export
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export
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Functor (GenCotambara ten p a) where
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map = rmap
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@ -153,11 +143,11 @@ CotambaraSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
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CotambaraSum = GenCotambara Either
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public export
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export
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cotambara : GenCostrong ten p => p :-> q -> p :-> GenCotambara ten q
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cotambara f = MkCotambara f
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public export
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export
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uncotambara : Tensor ten i => Profunctor q => p :-> GenCotambara ten q -> p :-> q
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uncotambara f p = proextract (f p)
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@ -174,27 +164,27 @@ record GenCopastro (ten, p : Type -> Type -> Type) a b where
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constructor MkCopastro
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runCopastro : forall q. GenCostrong ten q => p :-> q -> q a b
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public export
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export
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Profunctor (GenCopastro ten p) where
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dimap f g (MkCopastro h) = MkCopastro $ \n => dimap f g (h n)
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lmap f (MkCopastro h) = MkCopastro $ \n => lmap f (h n)
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rmap f (MkCopastro h) = MkCopastro $ \n => rmap f (h n)
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public export
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export
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ProfunctorFunctor (GenCopastro ten) where
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promap f (MkCopastro h) = MkCopastro $ \n => h (n . f)
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public export
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export
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ProfunctorMonad (GenCopastro ten) where
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propure p = MkCopastro ($ p)
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projoin p = MkCopastro $ \x => runCopastro p (\y => runCopastro y x)
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public export
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export
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GenCostrong ten (GenCopastro ten p) where
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costrongl (MkCopastro h) = MkCopastro $ \n => costrongl {ten} (h n)
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costrongr (MkCopastro h) = MkCopastro $ \n => costrongr {ten} (h n)
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public export
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export
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ProfunctorAdjunction (GenCopastro ten) (GenCotambara ten) where
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prounit p = MkCotambara id (propure {t=GenCopastro ten} p)
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procounit (MkCopastro h) = proextract (h id)
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@ -217,10 +207,10 @@ CopastroSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
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CopastroSum = GenCopastro Either
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public export
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export
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copastro : GenCostrong ten q => p :-> q -> GenCopastro ten p :-> q
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copastro f (MkCopastro h) = h f
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public export
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export
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uncopastro : Tensor ten i => GenCopastro ten p :-> q -> p :-> q
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uncopastro f x = f (MkCopastro ($ x))
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|
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|
@ -1,5 +1,6 @@
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module Data.Profunctor.Mapping
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import Control.Monad.Identity
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import Data.Morphisms
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import Data.Tensor
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import Data.Profunctor
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|
@ -8,9 +9,6 @@ import Data.Profunctor.Traversing
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%default total
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functor : Functor (\a => (a -> b) -> t)
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functor = MkFunctor (\f => (. (. f)))
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------------------------------------------------------------------------------
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-- Mapping interface
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------------------------------------------------------------------------------
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|
@ -22,7 +20,7 @@ functor = MkFunctor (\f => (. (. f)))
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||| * `map' . lmap f = lmap (map f) . map'`
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||| * `map' . rmap f = rmap (map f) . map'`
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||| * `map' . map' = map' @{Compose}`
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||| * `dimap Id runIdentity . map' = id`
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||| * `dimap Identity runIdentity . map' = id`
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public export
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interface (Traversing p, Closed p) => Mapping p where
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map' : Functor f => p a b -> p (f a) (f b)
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|
@ -30,21 +28,24 @@ interface (Traversing p, Closed p) => Mapping p where
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roam : ((a -> b) -> s -> t) -> p a b -> p s t
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roam f = dimap (flip f) ($ id) . map' @{%search} @{functor}
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where
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functor : Functor (\a => (a -> b) -> t)
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functor = MkFunctor (\f => (. (. f)))
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|
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|
||||
------------------------------------------------------------------------------
|
||||
-- Implementations
|
||||
-- Implementations for existing types
|
||||
------------------------------------------------------------------------------
|
||||
|
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|
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public export
|
||||
export
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Mapping Morphism where
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map' (Mor f) = Mor (map f)
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roam f (Mor x) = Mor (f x)
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||| A named implementation of `Mapping` for function types.
|
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||| Use this to avoid having to use a type wrapper like `Morphism`.
|
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public export
|
||||
export
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[Function] Mapping (\a,b => a -> b)
|
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using Traversing.Function Closed.Function where
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map' = map
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|
@ -52,7 +53,7 @@ public export
|
|||
|
||||
|
||||
------------------------------------------------------------------------------
|
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-- CofreeMapping
|
||||
-- Implementations for existing types
|
||||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
|
@ -63,44 +64,47 @@ record CofreeMapping p a b where
|
|||
constructor MkCFM
|
||||
runCFM : forall f. Functor f => p (f a) (f b)
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Profunctor (CofreeMapping p) where
|
||||
lmap f (MkCFM p) = MkCFM (lmap (map f) p)
|
||||
rmap f (MkCFM p) = MkCFM (rmap (map f) p)
|
||||
dimap f g (MkCFM p) = MkCFM (dimap (map f) (map g) p)
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Functor (CofreeMapping p a) where
|
||||
map = rmap
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor CofreeMapping where
|
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promap f (MkCFM p) = MkCFM (f p)
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||||
|
||||
public export
|
||||
export
|
||||
ProfunctorComonad CofreeMapping where
|
||||
proextract (MkCFM p) = p @{FunctorId}
|
||||
proextract (MkCFM p) = dimap Id runIdentity p
|
||||
produplicate (MkCFM p) = MkCFM $ MkCFM $ p @{Compose}
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||||
|
||||
public export
|
||||
export
|
||||
Symmetric ten => Profunctor p => GenStrong ten (CofreeMapping p) where
|
||||
strongr (MkCFM p) = MkCFM (p @{Compose {g=ten c} @{%search} @{MkFunctor mapSnd}})
|
||||
strongl (MkCFM p) = MkCFM (p @{Compose {g=(`ten` c)} @{%search} @{MkFunctor mapFst}})
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Closed (CofreeMapping p) where
|
||||
closed (MkCFM p) = MkCFM (p @{Compose {g = \b => x -> b} @{%search} @{MkFunctor (.)}})
|
||||
|
||||
roamCofree : Profunctor p => ((a -> b) -> s -> t) -> CofreeMapping p a b -> CofreeMapping p s t
|
||||
roamCofree f (MkCFM p) = MkCFM $ dimap (map (flip f)) (map ($ id)) $
|
||||
p @{Compose @{%search} @{functor}}
|
||||
where
|
||||
functor : Functor (\a => (a -> b) -> t)
|
||||
functor = MkFunctor (\f => (. (. f)))
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Traversing (CofreeMapping p) where
|
||||
traverse' (MkCFM p) = MkCFM (p @{Compose})
|
||||
wander f = roamCofree $ f @{ApplicativeId}
|
||||
wander f = roamCofree $ (runIdentity .) . f . (Id .)
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Mapping (CofreeMapping p) where
|
||||
map' (MkCFM p) = MkCFM (p @{Compose})
|
||||
roam = roamCofree
|
||||
|
@ -115,48 +119,51 @@ public export
|
|||
data FreeMapping : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
||||
MkFM : Functor f => (f y -> b) -> p x y -> (a -> f x) -> FreeMapping p a b
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor (FreeMapping p) where
|
||||
lmap f (MkFM l m r) = MkFM l m (r . f)
|
||||
rmap f (MkFM l m r) = MkFM (f . l) m r
|
||||
dimap f g (MkFM l m r) = MkFM (g . l) m (r . f)
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor FreeMapping where
|
||||
promap f (MkFM l m r) = MkFM l (f m) r
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorMonad FreeMapping where
|
||||
propure p = MkFM @{FunctorId} id p id
|
||||
propure p = MkFM runIdentity p Id
|
||||
projoin (MkFM l' (MkFM l m r) r') = MkFM @{Compose} (l' . map l) m (map r . r')
|
||||
|
||||
public export
|
||||
export
|
||||
Functor (FreeMapping p a) where
|
||||
map = rmap
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong Pair (FreeMapping p) where
|
||||
strongr (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||
strongl = dimap swap' swap' . strongr {p=FreeMapping p}
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong Either (FreeMapping p) where
|
||||
strongr (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||
strongl = dimap swap' swap' . strongr {p=FreeMapping p}
|
||||
|
||||
public export
|
||||
export
|
||||
Closed (FreeMapping p) where
|
||||
closed (MkFM l m r) = dimap Mor applyMor $ MkFM @{Compose} (map l) m (map r)
|
||||
|
||||
roamFree : ((a -> b) -> s -> t) -> FreeMapping p a b -> FreeMapping p s t
|
||||
roamFree f (MkFM l m r) = MkFM @{Compose @{functor}} (($ id) . map @{functor} l) m (map @{functor} r . flip f)
|
||||
where
|
||||
functor : Functor (\a => (a -> b) -> t)
|
||||
functor = MkFunctor (\f => (. (. f)))
|
||||
|
||||
public export
|
||||
export
|
||||
Traversing (FreeMapping p) where
|
||||
traverse' (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||
wander f = roamFree $ f @{ApplicativeId}
|
||||
wander f = roamFree $ (runIdentity .) . f . (Id .)
|
||||
|
||||
public export
|
||||
export
|
||||
Mapping (FreeMapping p) where
|
||||
map' (MkFM l m r) = MkFM @{Compose} (map l) m (map r)
|
||||
roam = roamFree
|
||||
|
|
|
@ -1,6 +1,5 @@
|
|||
module Data.Profunctor.Representable
|
||||
|
||||
import Control.Applicative.Const
|
||||
import Control.Monad.Identity
|
||||
import Data.Morphisms
|
||||
import Data.Profunctor
|
||||
|
@ -21,7 +20,7 @@ interface (Sieve p f, Strong p) => Representable p f | p where
|
|||
tabulate : (a -> f b) -> p a b
|
||||
|
||||
|
||||
||| A profunctor `p` is corepresentable if it is isomorphic to `Costar f` for some `f`.
|
||||
||| A profunctor `p` is representable if it is isomorphic to `Costar f` for some `f`.
|
||||
public export
|
||||
interface Cosieve p f => Corepresentable p f | p where
|
||||
cotabulate : (f a -> b) -> p a b
|
||||
|
@ -50,9 +49,9 @@ Representable Morphism Identity where
|
|||
||| A named implementation of `Representable` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
export
|
||||
[Function] Representable (\a,b => a -> b) Prelude.id
|
||||
[Function] Representable (\a,b => a -> b) Identity
|
||||
using Sieve.Function Strong.Function where
|
||||
tabulate = id
|
||||
tabulate = (runIdentity .)
|
||||
|
||||
export
|
||||
Functor f => Representable (Kleislimorphism f) f where
|
||||
|
@ -62,25 +61,9 @@ export
|
|||
Functor f => Representable (Star f) f where
|
||||
tabulate = MkStar
|
||||
|
||||
export
|
||||
Representable (Forget r) (Const r) where
|
||||
tabulate = MkForget . (runConst .)
|
||||
|
||||
export
|
||||
Corepresentable Morphism Identity where
|
||||
cotabulate f = Mor (f . Id)
|
||||
|
||||
namespace Corepresentable
|
||||
||| A named implementation of `Corepresentable` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
export
|
||||
[Function] Corepresentable (\a,b => a -> b) Prelude.id using Cosieve.Function where
|
||||
cotabulate = id
|
||||
|
||||
export
|
||||
Functor f => Corepresentable (Costar f) f where
|
||||
cotabulate = MkCostar
|
||||
|
||||
export
|
||||
Corepresentable (Coforget r) (Const r) where
|
||||
cotabulate = MkCoforget . (. MkConst)
|
||||
|
||||
|
|
|
@ -1,6 +1,5 @@
|
|||
module Data.Profunctor.Sieve
|
||||
|
||||
import Control.Applicative.Const
|
||||
import Control.Monad.Identity
|
||||
import Data.Morphisms
|
||||
import Data.Profunctor
|
||||
|
@ -30,44 +29,37 @@ interface (Profunctor p, Functor f) => Cosieve p f | p where
|
|||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Sieve Morphism Identity where
|
||||
sieve (Mor f) = Id . f
|
||||
|
||||
||| A named implementation of `Sieve` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
public export
|
||||
[Function] Sieve (\a,b => a -> b) Prelude.id using Profunctor.Function FunctorId where
|
||||
sieve = id
|
||||
export
|
||||
[Function] Sieve (\a,b => a -> b) Identity using Profunctor.Function where
|
||||
sieve = (Id .)
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Sieve (Kleislimorphism f) f where
|
||||
sieve = applyKleisli
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Sieve (Star f) f where
|
||||
sieve = applyStar
|
||||
|
||||
public export
|
||||
Sieve (Forget r) (Const r) where
|
||||
sieve (MkForget k) = MkConst . k
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Cosieve Morphism Identity where
|
||||
cosieve (Mor f) = f . runIdentity
|
||||
|
||||
namespace Cosieve
|
||||
||| A named implementation of `Cosieve` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
public export
|
||||
[Function] Cosieve (\a,b => a -> b) Prelude.id using Profunctor.Function FunctorId where
|
||||
cosieve = id
|
||||
export
|
||||
[Function] Cosieve (\a,b => a -> b) Identity using Profunctor.Function where
|
||||
cosieve = (. runIdentity)
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Cosieve (Costar f) f where
|
||||
cosieve = applyCostar
|
||||
|
||||
public export
|
||||
Cosieve (Coforget r) (Const r) where
|
||||
cosieve (MkCoforget k) = k . runConst
|
||||
|
|
|
@ -80,73 +80,58 @@ right : Choice p => p a b -> p (Either c a) (Either c b)
|
|||
right = strongr {ten=Either}
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
uncurry' : Strong p => p a (b -> c) -> p (a, b) c
|
||||
uncurry' = rmap (uncurry id) . first
|
||||
|
||||
public export
|
||||
export
|
||||
strong : Strong p => (a -> b -> c) -> p a b -> p a c
|
||||
strong f = dimap dup (uncurry $ flip f) . first
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- Implementations
|
||||
-- Implementations for existing types
|
||||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Bifunctor ten => GenStrong ten Morphism where
|
||||
strongl (Mor f) = Mor (mapFst f)
|
||||
strongr (Mor f) = Mor (mapSnd f)
|
||||
|
||||
||| A named implementation of `GenStrong` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
public export
|
||||
export
|
||||
[Function] Bifunctor ten => GenStrong ten (\a,b => a -> b)
|
||||
using Profunctor.Function where
|
||||
strongl = mapFst
|
||||
strongr = mapSnd
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => GenStrong Pair (Kleislimorphism f) where
|
||||
strongl (Kleisli f) = Kleisli $ \(a,c) => (,c) <$> f a
|
||||
strongr (Kleisli f) = Kleisli $ \(c,a) => (c,) <$> f a
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative f => GenStrong Either (Kleislimorphism f) where
|
||||
strongl (Kleisli f) = Kleisli $ either (map Left . f) (pure . Right)
|
||||
strongr (Kleisli f) = Kleisli $ either (pure . Left) (map Right . f)
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => GenStrong Pair (Star f) where
|
||||
strongl (MkStar f) = MkStar $ \(a,c) => (,c) <$> f a
|
||||
strongr (MkStar f) = MkStar $ \(c,a) => (c,) <$> f a
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative f => GenStrong Either (Star f) where
|
||||
strongl (MkStar f) = MkStar $ either (map Left . f) (pure . Right)
|
||||
strongr (MkStar f) = MkStar $ either (pure . Left) (map Right . f)
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong Either Tagged where
|
||||
strongl (Tag x) = Tag (Left x)
|
||||
strongr (Tag x) = Tag (Right x)
|
||||
|
||||
public export
|
||||
GenStrong Pair (Forget r) where
|
||||
strongl (MkForget k) = MkForget (k . fst)
|
||||
strongr (MkForget k) = MkForget (k . snd)
|
||||
|
||||
public export
|
||||
Monoid r => GenStrong Either (Forget r) where
|
||||
strongl (MkForget k) = MkForget (either k (const neutral))
|
||||
strongr (MkForget k) = MkForget (either (const neutral) k)
|
||||
|
||||
public export
|
||||
GenStrong Either (Coforget r) where
|
||||
strongl (MkCoforget k) = MkCoforget (Left . k)
|
||||
strongr (MkCoforget k) = MkCoforget (Right . k)
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- Tambara
|
||||
|
@ -160,26 +145,26 @@ record GenTambara (ten, p : Type -> Type -> Type) a b where
|
|||
constructor MkTambara
|
||||
runTambara : forall c. p (a `ten` c) (b `ten` c)
|
||||
|
||||
public export
|
||||
export
|
||||
Bifunctor ten => Profunctor p => Profunctor (GenTambara ten p) where
|
||||
dimap f g (MkTambara p) = MkTambara $ dimap (mapFst f) (mapFst g) p
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor (GenTambara ten) where
|
||||
promap f (MkTambara p) = MkTambara (f p)
|
||||
|
||||
public export
|
||||
export
|
||||
Tensor ten i => ProfunctorComonad (GenTambara ten) where
|
||||
proextract (MkTambara p) = dimap unitr.rightToLeft unitr.leftToRight p
|
||||
produplicate (MkTambara p) = MkTambara $ MkTambara $ dimap assocr assocl p
|
||||
|
||||
public export
|
||||
export
|
||||
Associative ten => Symmetric ten => Profunctor p => GenStrong ten (GenTambara ten p) where
|
||||
strongl (MkTambara p) = MkTambara $ dimap assocr assocl p
|
||||
strongr (MkTambara p) = MkTambara $ dimap (assocr . mapFst swap')
|
||||
(mapFst swap' . assocl) p
|
||||
|
||||
public export
|
||||
export
|
||||
Bifunctor ten => Profunctor p => Functor (GenTambara ten p a) where
|
||||
map = rmap
|
||||
|
||||
|
@ -201,11 +186,11 @@ TambaraSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
|
|||
TambaraSum = GenTambara Either
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
tambara : GenStrong ten p => p :-> q -> p :-> GenTambara ten q
|
||||
tambara @{gs} f x = MkTambara $ f $ strongl @{gs} x
|
||||
|
||||
public export
|
||||
export
|
||||
untambara : Tensor ten i => Profunctor q => p :-> GenTambara ten q -> p :-> q
|
||||
untambara f x = dimap unitr.rightToLeft unitr.leftToRight $ runTambara $ f x
|
||||
|
||||
|
@ -222,17 +207,17 @@ data GenPastro : (ten, p : Type -> Type -> Type) -> Type -> Type -> Type where
|
|||
MkPastro : (y `ten` z -> b) -> p x y -> (a -> x `ten` z) -> GenPastro ten p a b
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor (GenPastro ten p) where
|
||||
dimap f g (MkPastro l m r) = MkPastro (g . l) m (r . f)
|
||||
lmap f (MkPastro l m r) = MkPastro l m (r . f)
|
||||
rmap g (MkPastro l m r) = MkPastro (g . l) m r
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor (GenPastro ten) where
|
||||
promap f (MkPastro l m r) = MkPastro l (f m) r
|
||||
|
||||
public export
|
||||
export
|
||||
(Tensor ten i, Symmetric ten) => ProfunctorMonad (GenPastro ten) where
|
||||
propure x = MkPastro unitr.leftToRight x unitr.rightToLeft
|
||||
projoin (MkPastro {x=x',y=y',z=z'} l' (MkPastro {x,y,z} l m r) r') = MkPastro ll m rr
|
||||
|
@ -243,12 +228,12 @@ public export
|
|||
rr : a -> x `ten` (z' `ten` z)
|
||||
rr = mapSnd swap' . assocr . mapFst r . r'
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorAdjunction (GenPastro ten) (GenTambara ten) where
|
||||
prounit x = MkTambara (MkPastro id x id)
|
||||
procounit (MkPastro l (MkTambara x) r) = dimap r l x
|
||||
|
||||
public export
|
||||
export
|
||||
(Associative ten, Symmetric ten) => GenStrong ten (GenPastro ten p) where
|
||||
strongl (MkPastro {x,y,z} l m r) = MkPastro l' m r'
|
||||
where
|
||||
|
@ -281,11 +266,11 @@ PastroSum : (p : Type -> Type -> Type) -> Type -> Type -> Type
|
|||
PastroSum = GenPastro Either
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
pastro : GenStrong ten q => p :-> q -> GenPastro ten p :-> q
|
||||
pastro @{gs} f (MkPastro l m r) = dimap r l (strongl @{gs} (f m))
|
||||
|
||||
public export
|
||||
export
|
||||
unpastro : Tensor ten i => GenPastro ten p :-> q -> p :-> q
|
||||
unpastro f x = f (MkPastro unitr.leftToRight x unitr.rightToLeft)
|
||||
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
module Data.Profunctor.Traversing
|
||||
|
||||
import Control.Applicative.Const
|
||||
import Control.Monad.Identity
|
||||
import Data.Morphisms
|
||||
import Data.Tensor
|
||||
import Data.Profunctor
|
||||
|
@ -8,11 +8,6 @@ import Data.Profunctor
|
|||
%default total
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- Default implementation machinery
|
||||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
[FoldablePair] Foldable (Pair c) where
|
||||
foldr op init (_, x) = x `op` init
|
||||
foldl op init (_, x) = init `op` x
|
||||
|
@ -21,6 +16,14 @@ import Data.Profunctor
|
|||
[TraversablePair] Traversable (Pair c) using FoldablePair where
|
||||
traverse f (l, r) = (l,) <$> f r
|
||||
|
||||
[FoldableIdentity] Foldable Identity where
|
||||
foldr f i (Id x) = f x i
|
||||
foldl f i (Id x) = f i x
|
||||
null _ = False
|
||||
|
||||
[TraversableIdentity] Traversable Identity using FoldableIdentity where
|
||||
traverse f (Id x) = map Id (f x)
|
||||
|
||||
|
||||
record Bazaar a b t where
|
||||
constructor MkBazaar
|
||||
|
@ -45,7 +48,7 @@ Functor (Baz t b) where
|
|||
|
||||
|
||||
sold : Baz t a a -> t
|
||||
sold m = runBaz @{ApplicativeId} m id
|
||||
sold m = runIdentity (runBaz m Id)
|
||||
|
||||
Foldable (Baz t b) where
|
||||
foldr f i bz = runBaz bz @{appEndo} f i
|
||||
|
@ -57,11 +60,6 @@ Foldable (Baz t b) where
|
|||
Traversable (Baz t b) where
|
||||
traverse f bz = map (\m => MkBaz (runBazaar m)) $ runBaz bz @{Compose} $ \x => sell <$> f x
|
||||
|
||||
public export
|
||||
wanderDef : Profunctor p => (forall f. Traversable f => p a b -> p (f a) (f b))
|
||||
-> (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
|
||||
wanderDef tr f = dimap (\s => MkBaz $ \afb => f afb s) sold . tr
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- Traversing interface
|
||||
|
@ -83,41 +81,31 @@ interface (Strong p, Choice p) => Traversing p where
|
|||
traverse' = wander traverse
|
||||
|
||||
wander : (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
|
||||
wander = wanderDef traverse'
|
||||
wander f = dimap (\s => MkBaz $ \afb => f afb s) sold . traverse'
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- Implementations
|
||||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Traversing Morphism where
|
||||
traverse' (Mor f) = Mor (map f)
|
||||
wander f (Mor p) = Mor (f @{ApplicativeId} p)
|
||||
wander f (Mor p) = Mor (runIdentity . (f $ Id . p))
|
||||
|
||||
||| A named implementation of `Traversing` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
public export
|
||||
export
|
||||
[Function] Traversing (\a,b => a -> b) using Strong.Function where
|
||||
traverse' = map
|
||||
wander f = f @{ApplicativeId}
|
||||
wander f g = runIdentity . (f $ Id . g)
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative f => Traversing (Kleislimorphism f) where
|
||||
traverse' (Kleisli p) = Kleisli (traverse p)
|
||||
wander f (Kleisli p) = Kleisli (f p)
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative f => Traversing (Star f) where
|
||||
traverse' (MkStar p) = MkStar (traverse p)
|
||||
wander f (MkStar p) = MkStar (f p)
|
||||
|
||||
public export
|
||||
Monoid r => Traversing (Forget r) where
|
||||
traverse' (MkForget k) = MkForget (foldMap k)
|
||||
wander f (MkForget k) = MkForget (runConst . f (MkConst . k))
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- CofreeTraversing
|
||||
|
@ -131,45 +119,45 @@ record CofreeTraversing p a b where
|
|||
constructor MkCFT
|
||||
runCFT : forall f. Traversable f => p (f a) (f b)
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Profunctor (CofreeTraversing p) where
|
||||
lmap f (MkCFT p) = MkCFT (lmap (map f) p)
|
||||
rmap g (MkCFT p) = MkCFT (rmap (map g) p)
|
||||
dimap f g (MkCFT p) = MkCFT (dimap (map f) (map g) p)
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => GenStrong Pair (CofreeTraversing p) where
|
||||
strongr (MkCFT p) = MkCFT (p @{Compose @{%search} @{TraversablePair}})
|
||||
strongl = dimap swap' swap' . strongr {p=CofreeTraversing p}
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => GenStrong Either (CofreeTraversing p) where
|
||||
strongr (MkCFT p) = MkCFT (p @{Compose {f=Either c}})
|
||||
strongl = dimap swap' swap' . strongr {p=CofreeTraversing p}
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Traversing (CofreeTraversing p) where
|
||||
traverse' (MkCFT p) = MkCFT (p @{Compose})
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor CofreeTraversing where
|
||||
promap f (MkCFT p) = MkCFT (f p)
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorComonad CofreeTraversing where
|
||||
proextract (MkCFT p) = p @{TraversableId}
|
||||
proextract (MkCFT p) = dimap Id runIdentity $ p @{TraversableIdentity}
|
||||
produplicate (MkCFT p) = MkCFT $ MkCFT $ p @{Compose}
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor p => Functor (CofreeTraversing p a) where
|
||||
map = rmap
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
cofreeTraversing : Traversing p => p :-> q -> p :-> CofreeTraversing q
|
||||
cofreeTraversing f p = MkCFT $ f $ traverse' p
|
||||
|
||||
public export
|
||||
export
|
||||
uncofreeTraversing : Profunctor q => p :-> CofreeTraversing q -> p :-> q
|
||||
uncofreeTraversing f p = proextract $ f p
|
||||
|
||||
|
@ -185,40 +173,40 @@ public export
|
|||
data FreeTraversing : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
||||
MkFT : Traversable f => (f y -> b) -> p x y -> (a -> f x) -> FreeTraversing p a b
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor (FreeTraversing p) where
|
||||
lmap f (MkFT l m r) = MkFT l m (r . f)
|
||||
rmap f (MkFT l m r) = MkFT (f . l) m r
|
||||
dimap f g (MkFT l m r) = MkFT (g . l) m (r . f)
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong Pair (FreeTraversing p) where
|
||||
strongr (MkFT l m r) = MkFT @{Compose @{TraversablePair}} (map l) m (map r)
|
||||
strongl = dimap swap' swap' . strongr {p=FreeTraversing p}
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong Either (FreeTraversing p) where
|
||||
strongr (MkFT l m r) = MkFT @{Compose {t=Either c}} (map l) m (map r)
|
||||
strongl = dimap swap' swap' . strongr {p=FreeTraversing p}
|
||||
|
||||
public export
|
||||
export
|
||||
Traversing (FreeTraversing p) where
|
||||
traverse' (MkFT l m r) = MkFT @{Compose} (map l) m (map r)
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor FreeTraversing where
|
||||
promap f (MkFT l m r) = MkFT l (f m) r
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorMonad FreeTraversing where
|
||||
propure p = MkFT @{TraversableId} id p id
|
||||
propure p = MkFT @{TraversableIdentity} runIdentity p Id
|
||||
projoin (MkFT l' (MkFT l m r) r') = MkFT @{Compose} (l' . map l) m (map r . r')
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
freeTraversing : Traversing q => p :-> q -> FreeTraversing p :-> q
|
||||
freeTraversing fn (MkFT {f} l m r) = dimap r l (traverse' {f} (fn m))
|
||||
|
||||
public export
|
||||
export
|
||||
unfreeTraversing : FreeTraversing p :-> q -> p :-> q
|
||||
unfreeTraversing f p = f (MkFT @{TraversableId} id p id)
|
||||
unfreeTraversing f p = f (MkFT @{TraversableIdentity} runIdentity p Id)
|
||||
|
|
|
@ -59,7 +59,7 @@ p :-> q = forall a, b. p a b -> q a b
|
|||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor Morphism where
|
||||
dimap f g (Mor h) = Mor (g . h . f)
|
||||
lmap f (Mor g) = Mor (g . f)
|
||||
|
@ -68,13 +68,13 @@ Profunctor Morphism where
|
|||
namespace Profunctor
|
||||
||| A named implementation of `Profunctor` for function types.
|
||||
||| Use this to avoid having to use a type wrapper like `Morphism`.
|
||||
public export
|
||||
export
|
||||
[Function] Profunctor (\a,b => a -> b) where
|
||||
dimap f g h = g . h . f
|
||||
lmap = flip (.)
|
||||
rmap = (.)
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Profunctor (Kleislimorphism f) where
|
||||
dimap f g (Kleisli h) = Kleisli (map g . h . f)
|
||||
lmap f (Kleisli g) = Kleisli (g . f)
|
||||
|
@ -82,7 +82,7 @@ Functor f => Profunctor (Kleislimorphism f) where
|
|||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- New profunctor types
|
||||
-- Implementations for existing types
|
||||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
|
@ -95,27 +95,27 @@ record Star {0 k : Type} (f : k -> Type) a (b : k) where
|
|||
constructor MkStar
|
||||
applyStar : a -> f b
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Functor (Star f a) where
|
||||
map f (MkStar g) = MkStar (map f . g)
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative f => Applicative (Star f a) where
|
||||
pure = MkStar . const . pure
|
||||
MkStar f <*> MkStar g = MkStar (\x => f x <*> g x)
|
||||
|
||||
public export
|
||||
export
|
||||
Monad f => Monad (Star f a) where
|
||||
MkStar f >>= g = MkStar $ \x => do
|
||||
a <- f x
|
||||
applyStar (g a) x
|
||||
|
||||
public export
|
||||
export
|
||||
Contravariant f => Contravariant (Star f a) where
|
||||
contramap f (MkStar g) = MkStar (contramap f . g)
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Profunctor (Star f) where
|
||||
dimap f g (MkStar h) = MkStar (map g . h . f)
|
||||
lmap f (MkStar g) = MkStar (g . f)
|
||||
|
@ -128,20 +128,20 @@ record Costar {0 k : Type} (f : k -> Type) (a : k) b where
|
|||
constructor MkCostar
|
||||
applyCostar : f a -> b
|
||||
|
||||
public export
|
||||
export
|
||||
Functor (Costar f a) where
|
||||
map f (MkCostar g) = MkCostar (f . g)
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative (Costar f a) where
|
||||
pure = MkCostar . const
|
||||
MkCostar f <*> MkCostar g = MkCostar (\x => f x (g x))
|
||||
|
||||
public export
|
||||
export
|
||||
Monad (Costar f a) where
|
||||
MkCostar f >>= g = MkCostar (\x => applyCostar (g (f x)) x)
|
||||
|
||||
public export
|
||||
export
|
||||
Functor f => Profunctor (Costar f) where
|
||||
dimap f g (MkCostar h) = MkCostar (g . h . map f)
|
||||
lmap f (MkCostar g) = MkCostar (g . map f)
|
||||
|
@ -160,21 +160,21 @@ public export
|
|||
retag : Tagged a c -> Tagged b c
|
||||
retag (Tag x) = Tag x
|
||||
|
||||
public export
|
||||
export
|
||||
Functor (Tagged a) where
|
||||
map f (Tag x) = Tag (f x)
|
||||
|
||||
public export
|
||||
export
|
||||
Applicative (Tagged a) where
|
||||
pure = Tag
|
||||
Tag f <*> Tag x = Tag (f x)
|
||||
|
||||
public export
|
||||
export
|
||||
Monad (Tagged a) where
|
||||
join = runTagged
|
||||
Tag x >>= f = f x
|
||||
|
||||
public export
|
||||
export
|
||||
Foldable (Tagged a) where
|
||||
foldr f x (Tag y) = f y x
|
||||
foldl f x (Tag y) = f x y
|
||||
|
@ -183,130 +183,12 @@ Foldable (Tagged a) where
|
|||
toList (Tag x) = [x]
|
||||
foldMap f (Tag x) = f x
|
||||
|
||||
public export
|
||||
export
|
||||
Traversable (Tagged a) where
|
||||
traverse f (Tag x) = map Tag (f x)
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor Tagged where
|
||||
dimap _ f (Tag x) = Tag (f x)
|
||||
lmap = const retag
|
||||
rmap f (Tag x) = Tag (f x)
|
||||
|
||||
|
||||
||| `Forget r` is equivalent to `Star (Const r)`.
|
||||
public export
|
||||
record Forget {0 k : Type} r a (b : k) where
|
||||
constructor MkForget
|
||||
runForget : a -> r
|
||||
|
||||
public export
|
||||
reforget : Forget r a b -> Forget r a c
|
||||
reforget (MkForget k) = MkForget k
|
||||
|
||||
public export
|
||||
Functor (Forget r a) where
|
||||
map _ = reforget
|
||||
|
||||
public export
|
||||
Contravariant (Forget {k=Type} r a) where
|
||||
contramap _ = reforget
|
||||
|
||||
public export
|
||||
Monoid r => Applicative (Forget r a) where
|
||||
pure _ = MkForget (const neutral)
|
||||
MkForget f <*> MkForget g = MkForget (f <+> g)
|
||||
|
||||
public export
|
||||
Monoid r => Monad (Forget {k=Type} r a) where
|
||||
join = reforget
|
||||
(>>=) = reforget .: const
|
||||
|
||||
public export
|
||||
Foldable (Forget r a) where
|
||||
foldr _ x _ = x
|
||||
foldl _ x _ = x
|
||||
null = const True
|
||||
foldlM _ x _ = pure x
|
||||
toList _ = []
|
||||
foldMap _ _ = neutral
|
||||
|
||||
public export
|
||||
Traversable (Forget r a) where
|
||||
traverse _ = pure . reforget
|
||||
|
||||
public export
|
||||
Profunctor (Forget r) where
|
||||
dimap f _ (MkForget k) = MkForget (k . f)
|
||||
lmap f (MkForget k) = MkForget (k . f)
|
||||
rmap = map
|
||||
|
||||
|
||||
||| `Coforget r` is equivalent to `Costar (Const r)`.
|
||||
public export
|
||||
record Coforget {0 k : Type} r (a : k) b where
|
||||
constructor MkCoforget
|
||||
runCoforget : r -> b
|
||||
|
||||
public export
|
||||
recoforget : Coforget r a c -> Coforget r b c
|
||||
recoforget (MkCoforget k) = MkCoforget k
|
||||
|
||||
public export
|
||||
Functor (Coforget r a) where
|
||||
map f (MkCoforget k) = MkCoforget (f . k)
|
||||
|
||||
public export
|
||||
Bifunctor (Coforget r) where
|
||||
bimap _ f (MkCoforget k) = MkCoforget (f . k)
|
||||
mapFst _ = recoforget
|
||||
mapSnd = map
|
||||
|
||||
public export
|
||||
Applicative (Coforget r a) where
|
||||
pure = MkCoforget . const
|
||||
MkCoforget f <*> MkCoforget g = MkCoforget (\r => f r (g r))
|
||||
|
||||
public export
|
||||
Monad (Coforget r a) where
|
||||
MkCoforget k >>= f = MkCoforget (\r => runCoforget (f $ k r) r)
|
||||
|
||||
public export
|
||||
Profunctor (Coforget r) where
|
||||
dimap _ f (MkCoforget k) = MkCoforget (f . k)
|
||||
lmap _ = recoforget
|
||||
rmap = map
|
||||
|
||||
|
||||
------------------------------------------------------------------------------
|
||||
-- Identity functor
|
||||
------------------------------------------------------------------------------
|
||||
|
||||
-- A few convenience definitions for use in other modules.
|
||||
|
||||
public export
|
||||
[FunctorId] Functor Prelude.id where
|
||||
map = id
|
||||
|
||||
public export
|
||||
[ApplicativeId] Applicative Prelude.id using FunctorId where
|
||||
pure = id
|
||||
(<*>) = id
|
||||
|
||||
public export
|
||||
[MonadId] Monad Prelude.id using ApplicativeId where
|
||||
join = id
|
||||
(>>=) = flip id
|
||||
|
||||
public export
|
||||
[FoldableId] Foldable Prelude.id where
|
||||
foldr = flip
|
||||
foldl = id
|
||||
null _ = False
|
||||
foldlM = id
|
||||
toList = pure
|
||||
foldMap = id
|
||||
|
||||
public export
|
||||
[TraversableId] Traversable Prelude.id using FunctorId FoldableId where
|
||||
traverse = id
|
||||
|
|
|
@ -20,69 +20,69 @@ record Yoneda p a b where
|
|||
constructor MkYoneda
|
||||
runYoneda : forall x, y. (x -> a) -> (b -> y) -> p x y
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor (Yoneda p) where
|
||||
lmap f (MkYoneda p) = MkYoneda $ \l,r => p (f . l) r
|
||||
rmap f (MkYoneda p) = MkYoneda $ \l,r => p l (r . f)
|
||||
dimap f g (MkYoneda p) = MkYoneda $ \l,r => p (f . l) (r . g)
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor Yoneda where
|
||||
promap f (MkYoneda p) = MkYoneda $ f .: p
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorMonad Yoneda where
|
||||
propure p = MkYoneda $ \l,r => dimap l r p
|
||||
projoin (MkYoneda p) = p id id
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorComonad Yoneda where
|
||||
proextract (MkYoneda p) = p id id
|
||||
produplicate p = MkYoneda $ \l,r => dimap l r p
|
||||
|
||||
||| A witness that `Yoneda p` and `p` are equivalent when `p` is a profunctor.
|
||||
public export
|
||||
export
|
||||
yonedaEqv : Profunctor p => p a b <=> Yoneda p a b
|
||||
yonedaEqv = MkEquivalence propure proextract
|
||||
|
||||
public export
|
||||
export
|
||||
yonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
||||
p (q a b) (r a' b') -> p (Yoneda q a b) (Yoneda r a' b')
|
||||
yonedaIso = dimap proextract propure
|
||||
|
||||
public export
|
||||
export
|
||||
Functor (Yoneda p a) where
|
||||
map = rmap
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong ten p => GenStrong ten (Yoneda p) where
|
||||
strongl = propure . strongl {ten,p} . proextract
|
||||
strongr = propure . strongr {ten,p} . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
GenCostrong ten p => GenCostrong ten (Yoneda p) where
|
||||
costrongl = propure . costrongl {ten,p} . proextract
|
||||
costrongr = propure . costrongr {ten,p} . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Closed p => Closed (Yoneda p) where
|
||||
closed = propure . closed . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Traversing p => Traversing (Yoneda p) where
|
||||
traverse' = propure . traverse' . proextract
|
||||
wander f = propure . wander f . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Mapping p => Mapping (Yoneda p) where
|
||||
map' = propure . map' . proextract
|
||||
roam f = propure . roam f . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Sieve p f => Sieve (Yoneda p) f where
|
||||
sieve = sieve . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Cosieve p f => Cosieve (Yoneda p) f where
|
||||
cosieve = cosieve . proextract
|
||||
|
||||
|
@ -98,68 +98,68 @@ data Coyoneda : (p : Type -> Type -> Type) -> Type -> Type -> Type where
|
|||
MkCoyoneda : (a -> x) -> (y -> b) -> p x y -> Coyoneda p a b
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Profunctor (Coyoneda p) where
|
||||
lmap f (MkCoyoneda l r p) = MkCoyoneda (l . f) r p
|
||||
rmap f (MkCoyoneda l r p) = MkCoyoneda l (f . r) p
|
||||
dimap f g (MkCoyoneda l r p) = MkCoyoneda (l . f) (g . r) p
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorFunctor Coyoneda where
|
||||
promap f (MkCoyoneda l r p) = MkCoyoneda l r (f p)
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorMonad Coyoneda where
|
||||
propure = MkCoyoneda id id
|
||||
projoin (MkCoyoneda l r p) = dimap l r p
|
||||
|
||||
public export
|
||||
export
|
||||
ProfunctorComonad Coyoneda where
|
||||
proextract (MkCoyoneda l r p) = dimap l r p
|
||||
produplicate = MkCoyoneda id id
|
||||
|
||||
||| A witness that `Coyoneda p` and `p` are equivalent when `p` is a profunctor.
|
||||
public export
|
||||
export
|
||||
coyonedaEqv : Profunctor p => p a b <=> Coyoneda p a b
|
||||
coyonedaEqv = MkEquivalence propure proextract
|
||||
|
||||
public export
|
||||
export
|
||||
coyonedaIso : (Profunctor q, Profunctor r) => forall p. Profunctor p =>
|
||||
p (q a b) (r a' b') -> p (Coyoneda q a b) (Coyoneda r a' b')
|
||||
coyonedaIso = dimap proextract propure
|
||||
|
||||
public export
|
||||
export
|
||||
Functor (Coyoneda p a) where
|
||||
map = rmap
|
||||
|
||||
public export
|
||||
export
|
||||
GenStrong ten p => GenStrong ten (Coyoneda p) where
|
||||
strongl = propure . strongl {ten,p} . proextract
|
||||
strongr = propure . strongr {ten,p} . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
GenCostrong ten p => GenCostrong ten (Coyoneda p) where
|
||||
costrongl = propure . costrongl {ten,p} . proextract
|
||||
costrongr = propure . costrongr {ten,p} . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Closed p => Closed (Coyoneda p) where
|
||||
closed = propure . closed . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Traversing p => Traversing (Coyoneda p) where
|
||||
traverse' = propure . traverse' . proextract
|
||||
wander f = propure . wander f . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Mapping p => Mapping (Coyoneda p) where
|
||||
map' = propure . map' . proextract
|
||||
roam f = propure . roam f . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Sieve p f => Sieve (Coyoneda p) f where
|
||||
sieve = sieve . proextract
|
||||
|
||||
public export
|
||||
export
|
||||
Cosieve p f => Cosieve (Coyoneda p) f where
|
||||
cosieve = cosieve . proextract
|
||||
|
|
|
@ -58,16 +58,16 @@ interface Associative ten => Tensor ten i | ten where
|
|||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Associative Pair where
|
||||
assocl (x,(y,z)) = ((x,y),z)
|
||||
assocr ((x,y),z) = (x,(y,z))
|
||||
|
||||
public export
|
||||
export
|
||||
Symmetric Pair where
|
||||
swap' = swap
|
||||
|
||||
public export
|
||||
export
|
||||
Tensor Pair () where
|
||||
unitl = MkEquivalence snd ((),)
|
||||
unitr = MkEquivalence fst (,())
|
||||
|
@ -78,7 +78,7 @@ Tensor Pair () where
|
|||
------------------------------------------------------------------------------
|
||||
|
||||
|
||||
public export
|
||||
export
|
||||
Associative Either where
|
||||
assocl (Left x) = Left (Left x)
|
||||
assocl (Right (Left x)) = Left (Right x)
|
||||
|
@ -88,11 +88,11 @@ Associative Either where
|
|||
assocr (Left (Right x)) = Right (Left x)
|
||||
assocr (Right x) = Right (Right x)
|
||||
|
||||
public export
|
||||
export
|
||||
Symmetric Either where
|
||||
swap' = either Right Left
|
||||
|
||||
public export
|
||||
export
|
||||
Tensor Either Void where
|
||||
unitl = MkEquivalence (either absurd id) Right
|
||||
unitr = MkEquivalence (either id absurd) Left
|
||||
|
|
|
@ -1,7 +1,5 @@
|
|||
package profunctors
|
||||
version = 1.1.2
|
||||
|
||||
brief = "Profunctors for Idris2"
|
||||
version = 1.0.0
|
||||
|
||||
authors = "Kiana Sheibani"
|
||||
license = "MIT"
|
||||
|
|
Loading…
Reference in a new issue